correction of references (was: L. E. J. Brouwer and the Sub-Axiomatic Foundations of Mathematics)

José Manuel Rodríguez Caballero josephcmac at
Mon Mar 6 12:15:08 EST 2023

In a previous post I wrote:

> For example, in the paper "The Number Field Sieve for Integer
> Factorization" by A.K. Lenstra and H.W. Lenstra, computer science
> algorithms are used to factorize integers, leading to significant progress
> in number theory [3].

and I cited the paper

> [3] Lenstra, A.K. and Lenstra, H.W. "The Number Field Sieve for Integer
> Factorization." Proceedings of the 22nd Annual ACM Symposium on Theory of
> Computing, 1990, pp. 564-572.

it was a mistake. I meant the paper:

> [3] Lenstra, Arjen K., et al. "The factorization of the ninth Fermat
> number." *Mathematics of Computation* 61.203 (1993): 319-349.

Concerning the papers cited in the quote from the ChatGPT auto-reply to
Patrik's post,

> In support of the idea of separating mathematics and computer science, I
> would like to cite the following papers:
> E. Reck, ?Why Philosophy Matters for Mathematical Practice,? in The
> Philosophy of Mathematics Today, eds. M. Otte and M. Panza (Oxford
> University Press, 1997), 281-301.
> H. G. Dales, ?The Separation of Mathematics from Philosophy,? in Logic
> Colloquium '77, ed. P. Erd?s, A. Hajnal, and V. T. S?s (North-Holland
> Publishing Company, 1978), 19-39.
> J. P. Burgess, ?Why I Am Not a Constructivist,? in Logic, Methodology and
> Philosophy of Science IX, ed. L. Magnes and E. Stadler (Springer, 1994),
> 315-324.

I think it's ChatGPT's responsibility whether these citations are right,
since I presented the quote as a Turing test assessment, not as my claim.
After the post, I searched for these papers on Google because I was curious
about the subject, and I was not able to find them. This was a surprise for

Kind regards,
Jose M.
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